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Let f: X rarr Y If there exists a map ...

Let f: `X rarr Y`
If there exists a map g:Y `rarr` X such that gof = `id_(X)` and fog = `id_(y)`, then show that
f is bijective and (ii) `g =f^(-1)`

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ARIHANT PUBLICATION-RELATIONS AND FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS ( Exercise 1 (b))
  1. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  2. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  3. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

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  4. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  5. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-...

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  6. Let f(x) = sqrt(x) and g(x) = 1 -x^(2). Show that hgof only on R(0)=...

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  7. Find the composition fog and gof and test whether fog = gof when f and...

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  8. Find the composition fog and gof and test whether fog = gof when f and...

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  9. Find the composition fog and gof and test whether fog = gof when f and...

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  10. Find the composition fog and gof and test whether fog = gof when f and...

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  11. Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even...

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  12. Express each of e^x function as the sum of an even function and an odd...

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  13. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  14. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  15. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  16. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  17. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  18. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

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  19. Construct an example to show that f(A nn B )!= f(A) nn f(B) where A nn...

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  20. Prove that for any f:X rarr Y , f o idx = f =idY of.

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